On strong measure zero subsets of {}^kappa 2 .

Details On strong measure zero subsets of {}^kappa 2 . On strong measure zero subsets of {}^kappa 2 .

1997-10-15

arxiv.org/abs/math/9710218v1

Mathematics

Logic

Scientific paper

This paper answers three questions posed by the first author. In Theorem 2.6 we show that the family of strong measure zero subsets of {}^{omega_1}2 is 2^{aleph_1}-additive under GMA and CH. In Theorem 3.1 we prove that the generalized Borel conjecture is false in {}^{omega_1}2 assuming ZFC+CH. Next, in Theorem 4.2, we show that the family of subsets of {}^{omega_1}2 with the property of Baire is not closed under the Souslin operation.

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